Surds

If $\frac{{\left\{{\left(p+1\right)}^2\right\}}^3}{{(p+1)}^5}-\frac{3^2}{5} = q,$ then:

Find the value of $6\times \sqrt[4]{16} by \sqrt[4]{81}.$

Find the division $\sqrt[4]{256} by \sqrt[4]{16}.$

Find the division of $\sqrt[2]{5} by \sqrt[2]{2}-1.$

Find the division of $\sqrt[2]{15} by \sqrt[2]{3}.$

Find the division of $\sqrt[2]{12} by \sqrt[2]{3}$.

Find the value of: ${\left(\frac{5^{\mathrm{x}}}{5^{\mathrm{y}}}\right)}^{\mathrm{x}+\mathrm{y}}\times {\left(\frac{5^{\mathrm{y}}}{5^{\mathrm{z}}}\right)}^{\mathrm{y}+\mathrm{z}}\times {\left(\frac{5^{\mathrm{z}}}{5^{\mathrm{x}}}\right)}^{\mathrm{x}+\mathrm{z}}$.

If ${\mathrm{a}}^{{\mathrm{a}}^{\frac{9}{4}}}={\left( {\mathrm{a}}^{\frac{9}{4}}\right)}^{\mathrm{a}}$, Then find the value of $\mathrm{a}$.

If $x=\frac{2\sqrt{2}}{3}$, find the value of $\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}-\sqrt{1-x}}$..

Simplify :

${\left(0.004096\right)}^{\frac{1}{6}}+{\left(2187\right)}^{\frac{1}{7}}$

Simplify the following:

${\left(\sqrt[2]{\sqrt[4]{7^6}}\right)}^{12}\times {\left(\sqrt[5]{\sqrt[3]{7^4}}\right)}^{30}$ 

Find the value of  $\sqrt{72+\sqrt{72+\sqrt{72+..........}}}$. 

Simplify: $\frac{{13}^{{\displaystyle \frac{2}{3}}}\times \sqrt[3]{{13}^2}\times \sqrt[3]{{13}^7}}{\sqrt[3]{13}\times \sqrt[3]{{13}^4}}$

Simplify: ${512}^{0.25}\times {64}^{0.20}÷8^{0.15}$

If the value of  $\sqrt{30}$ is approximately $5.477$, then what is the approximate value of  $\sqrt{\frac{5}{6}}$?

$$1-\left( \cfrac { 1+\sqrt { 3 } }{ 2 } -\cfrac { 1 }{ \sqrt { 3 } +1 } \right) $$ is equal to -